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A mathematical statement that one quantity is greater than or less than another. "a is less than b" is denoted a<b, and "a is greater than b" is denoted a>b. "a is less than ...

The infimum is the greatest lower bound of a set S, defined as a quantity m such that no member of the set is less than m, but if epsilon is any positive quantity, however ...

In statistical mechanics, the two-dimensional Ising model is a popular tool used to study the dipole moments of magnetic spins. The Ising model in two dimensions is a type of ...

The Jacobi symbol, written (n/m) or (n/m) is defined for positive odd m as (n/m)=(n/(p_1))^(a_1)(n/(p_2))^(a_2)...(n/(p_k))^(a_k), (1) where m=p_1^(a_1)p_2^(a_2)...p_k^(a_k) ...

The Lotka-Volterra equations describe an ecological predator-prey (or parasite-host) model which assumes that, for a set of fixed positive constants A (the growth rate of ...

A Lyapunov function is a scalar function V(y) defined on a region D that is continuous, positive definite, V(y)>0 for all y!=0), and has continuous first-order partial ...

The minimal polynomial of a matrix A is the monic polynomial in A of smallest degree n such that p(A)=sum_(i=0)^nc_iA^i=0. (1) The minimal polynomial divides any polynomial q ...

A type of integral containing gamma functions in its integrand. A typical such integral is given by ...

Noncommutative topology is a recent program having important and deep applications in several branches of mathematics and mathematical physics. Because every commutative ...

A surface such as the Möbius strip or Klein bottle (Gray 1997, pp. 322-323) on which there exists a closed path such that the directrix is reversed when moved around this ...